So, how does the population grow?
Time is candy, so I've put tl;dr at the bottom and made some graphs first:
No techs bonuses in that gif, but here's a munchkin race - "just" high growth rate vs maximum possible with advanced cloning and nano-bodies at 10lvl:
And now it's time for tl;dr.
Let's assume colony never experiences starvation.
They never should.
Then, a colony goes through 4 stages of growth:
1) Initial spurt, from 50k to 10m.
- low growth rate - each turn population is x1.5 from previous turn
- average growth rate - each turn population is x2 from previous turn
- high growth rate - each turn population is x3 from previous turn
2) Young colony, from 10m to 1b.
- low - x1.025
- average - x1.05
- high - x1.1
3) Mature colony, from 1b to 3/4 of planet's current capacity
- low - x1.01
- average - x1.02
- high - x1.04
4) Overcrowded colony, from 3/4 of planet's current capacity to full
- low - x1.0025
- average - x1.005
- high - x1.01
So, when average colony gets its 100m, high growth colony will hit billion next turn.
And when low gets 100m, average is at 735m and high will hit 5b next turn.
Bonuses/debuffs from tech and environment are shown when you view a planet (or right click in the planets tab in colony view) and are applied in a peculiar way.
Let's assume we have a young colony with average rate with bonus growth 60%.
That means that 0.05 (from 1.05) is multiplied by 1.6 (from 60% bonus) and we get x1.08 each turn.
Maximum bonus possible seems for me to be 214% with all relevant techs at lvl10.
As bonuses (including racial) are just summarized, so looks like terraforming growth bonus isn't working.